Finsler Metric

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if

1. L(x,y) is differentiable at y!=0,

2. L(x,lambday)=|lambda|L(x,y) for any element (x,y) in T(M) and any real number lambda,

3. Denoting the metric


then g_(ij) is a positive definite matrix.

A smooth manifold M with a Finsler metric is called a Finsler space.

See also

Finsler Space, Smooth Manifold, Tangent Bundle

Explore with Wolfram|Alpha


Iyanaga, S. and Kawada, Y. (Eds.). "Finsler Spaces." §161 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 540-542, 1980.

Referenced on Wolfram|Alpha

Finsler Metric

Cite this as:

Weisstein, Eric W. "Finsler Metric." From MathWorld--A Wolfram Web Resource.

Subject classifications